Quotation fragment

Why we are here

.. I can live with doubt and uncertainty and not knowing. I think it's much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of certainty about different things, but I'm not absolutely sure of anything and there are many things I don't know anything about, such as whether it means anything to ask why we're here, and what the question might mean. I might think about it a little bit and if I can't figure it out, then I go on to something else, but I don't have to know and answer, I don't feel frightened by not knowing things, by being lost in a mysterious universe without having any purpose, which is the way it really is so far as I can tell. It doesn't frighten me.

Source: edited transcript of an interview with Richard Feynman made for the BBC television program Horizon in 1981, in Richard Feynman, the pleasure of finding things out, pg. 25.

In order to progress / Live and not know

The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of great importance, I think. When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is in some doubt. We have found it of paramount importance that in order to progress we must recognize the ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty - some most unsure, some nearly sure, none absolutely certain.

Now, we scientists are used to this, and we take it for granted that it is perfectly consistent to be unsure - that it is possible to live and not know. But I don't know everybody realizes that this is true. Our freedom to doubt was born of a struggle against authority in the early days of science. It was a very deep and very strong struggle. Permit us to question - to doubt, that's all - not to be sure. And I think it is important that we do not forget the importance of this struggle and thus perhaps lose what we have gained.

Source: What Do You Care What Other People Think? Further Adventures of a Curious Character by Richard Feynman as told to Ralph Leighton. In Richard Feynman, the pleasure of finding things out, pg. 146.

Two great heritages

Western civilization, it seems to me, stands by two great heritages. One is the scientific spirit of adventure - the adventure into the unknown, an unknown which must be recognized as being unknown in order to be explored; the demand that the unanswerable mysteries of the universe remain unanswered; the attitude that all is uncertain; to summarize it - the humility of the intellect. The other great heritage is Christian ethics - the basis of action on love, the brotherhood of all men, the value of the individual - the humility of the spirit.

These two heritages are logically, thoroughly consistent. But logic is not all, one needs one's heart to follow an idea. If people are going back to religion, what are they going back to? Is the modern church a place to give comfort to a man who doubts God - more, one who disbelieves in God? Is the modern church a place to give comfort and encouragement to the value of such doubts? So far, have we not drawn strength and comfort to maintain the one or the other of these consistent heritages in a way which attacks the values of the other? Is this unavoidable? How can we draw inspiration to support these two pillars of Western civilization so that they may stand together in full vigor, mutually unafraid? Is this not the central problem of our time?

Source: The Relation of Science and Religion by Richard Feynman, originally published by Caltech in Engineering and Science magazine. In Richard Feynman, the pleasure of finding things out, pg. 256.


As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

- Albert Einstein
(found in the "fortune-cookie" collection; source?)

I had a feeling once about mathematics -- that I saw it all. Depth beyond depth was revealed to me -- the Byss and the Abyss. I saw -- as one might see the transit of Venus or even the Lord Mayor's Show -- a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why tergiversation was inevitable -- but it was after dinner and I let it go.

- Winston Churchill
(found in the "fortune-cookie" collection; source?)

Mathematics, rightly viewed, possesses not only truth but supreme beauty -- a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, without the gorgeous trapping of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

- Bertrand Russell
(found in the "fortune-cookie" collection; source?)

The startling truth finally became apparent, and it was this: Numbers written on restaurant checks within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single statement took the scientific world by storm. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure, and the science of mathematics was put back by years.

- Douglas Adams

One of the ingredients in their analysis was a quantitative bound on the condition number of an arbitrary matrix when it is perturbed by a random gaussian perturbation; the point being that random perturbation can often make an ill-conditioned matrix better behaved. (This is perhaps analogous in some ways to the empirical experience that some pieces of machinery work better after being kicked.)

- Terry Tao, http://terrytao.wordpress.com/2010/08/20/spielman-meyer-nirenberg/

Modern art

[In Serra's case you can also call it democratic art because]

.. it sticks to pure form that requires no previous expertise to grasp. There's no coy narrative, no insider joke or historical allusion or meta-art theme. There's none of what Serra disdainfully calls, in the show's catalogue, "post-Pop Surrealism," by which he lumps together all contemporary art that leans for a crutch on language and Duchamp.

- Michael Kimmelman, International Herald Tribune, Tuesday, June 5, 2007

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